1 2 3 4 5 6 7 8 9 10 Government agencies keep data about the income distribution of the population. The Watson family and waker farnily live in a county with son0 farlies. Toe Watson family's income is at the \( 29^{\text {th }} \) percentile. The Walker family's incerme is at the \( 44^{\text {th }} \) percentile. (a) Which of the following must be true about the Watson family's and the Walker family's incomes? The Walker farnily earns \( \$ 15,000 \) more than the Watson family. The Watson family earns \( \$ 15,000 \) more than the Waliker family. Both the Watson family and the Walker famlly earn more than the median income. Both the Watson family and the Walker family earn less than the median income. (b) Which of the following must be true about the Watson famlly's income? The Watson family earns about \( 29 \% \) of the highest income in their county. The Watson family's income is in the top half of incomes in their county. The Watson farnlly earns \( \$ 29,000 \). The Watson family earns less than about \( 71 \% \) of families in their county.
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When it comes to income percentiles, knowing how they relate to the broader population can provide some clarity. In this scenario, a family at the \( 29^{\text{th}} \) percentile earns less than 29% of all families in the county. Hence, they are above the bottom 29%, which means there is a significant portion that earns more, confirming that both the Watson family and Walker family likely earn below the median income. Percentiles can be tricky! Remember that being at the \( 29^{\text{th}} \) percentile means the Watson family earns less than a solid chunk of their neighbors, while the Walker family, sitting at the \( 44^{\text{th}} \) percentile, has a bit more to work with—but they’re both below the median threshold. It's a subtle game of numbers!
